Geodesic
Theoretical analysis of steady state genetic algorithms
Applications of Mathematics, Tome 59 (2014) no. 5, pp. 509-525.

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Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are given under which the SSGA heuristic converges to the population consisting of copies of the best chromosome.
DOI : 10.1007/s10492-014-0069-z
Classification : 60J10, 60J20, 68T05, 68W20, 90C59
Keywords: genetic algorithm; Markov chain; random heuristic search 
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Agapie, Alexandru; Wright, Alden H. Theoretical analysis of steady state genetic algorithms. Applications of Mathematics, Tome 59 (2014) no. 5, pp. 509-525. doi : 10.1007/s10492-014-0069-z. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0069-z/

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